At Charlie's Cinema, a total of 1,200 adult and child movie tickets were sold to bring in $10,875 in ticket sales one evening. If each child ticket costs $7.50 and each adult ticket costs $10.00, how many adult tickets were sold that evening?

Question

At Charlie's Cinema, a total of 1,200 adult and child movie tickets were sold to bring in  $10,875 in ticket sales one evening. If each child ticket costs  $7.50 and each adult ticket costs  $10.00, how many adult tickets were sold that evening?

Bytelearn · Accepted Answer

Equations given: Let's denote the number of child tickets sold as C and the number of adult tickets sold as A. We are given two equations based on the total number of tickets sold and the total revenue from ticket sales: 1. C + A = 1,200 (total tickets equation) 2. 7.50C + 10A = 10,875 (total revenue equation) We need to solve this system of equations to find the value of A, which represents the number of adult tickets sold.Rearranging total tickets equation: First, we can rearrange the total tickets equation to express C in terms of A: C = 1,200 - A This will allow us to substitute the value of C in the total revenue equation.Substituting C into total revenue equation: Now, let's substitute C = 1,200 - A into the total revenue equation: 7.50(1,200 - A) + 10A = 10,875 Expanding this, we get: 9,000 - 7.50A + 10A = 10,875 Combining like terms, we have: 2.50A = 10,875 - 9,000Expanding and combining like terms: Next, we calculate the difference: 10,875 - 9,000 = 1,875 So, the equation now is: 2.50A = 1,875Calculating the difference: To find A, we divide both sides of the equation by 2.50: A = 1,875 / 2.50 Calculating this, we get: A = 750Dividing both sides of the equation: We have found that the number of adult tickets sold, A, is 750. To ensure we haven't made any mistakes, we can check our work by substituting A back into the original total tickets equation: C + A = 1,200 C + 750 = 1,200 C = 1,200 - 750 C = 450 Since C represents the number of child tickets, we can also check the total revenue by calculating: 7.50C + 10A = 7.50(450) + 10(750) = 3,375 + 7,500 = 10,875 The total revenue checks out, so our solution for A is correct.

At Charlie's Cinema, a total of $1$ , $200$ adult and child movie tickets were sold to bring in $\$ 10,875$ in ticket sales one evening. If each child ticket costs $\$ 7.50$ and each adult ticket costs $\$ 10.00$ , how many adult tickets were sold that evening?

Full solution

More problems from Approximation percent word problems

Related topics

At Charlie's Cinema, a total of 111,200200200 adult and child movie tickets were sold to bring in $10,875 \$ 10,875 $10,875 in ticket sales one evening. If each child ticket costs $7.50 \$ 7.50 $7.50 and each adult ticket costs $10.00 \$ 10.00 $10.00, how many adult tickets were sold that evening?

At Charlie's Cinema, a total of $1$ , $200$ adult and child movie tickets were sold to bring in $\$ 10,875$ in ticket sales one evening. If each child ticket costs $\$ 7.50$ and each adult ticket costs $\$ 10.00$ , how many adult tickets were sold that evening?